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A certain structure of Artin groups and the isomorphism conjecture

Part of: Whitehead groups and $K_1$ Differential topology $K$-theory of forms Topological manifolds Special aspects of infinite or finite groups

Published online by Cambridge University Press:  21 May 2020

S.K. Roushon
S.K. Roushon*
Affiliation:
School of Mathematics, Tata Institute, Homi Bhabha Road, Mumbai 400005, India URL: http://www.math.tifr.res.in/~roushon
*
e-mail: roushon@math.tifr.res.in
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Abstract

We observe an inductive structure in a large class of Artin groups of finite real, complex and affine types and exploit this information to deduce the Farrell–Jones isomorphism conjecture for these groups.

Keywords

Artin groupisomorphism conjectureWhitehead groupreduced projective class groupsurgery obstruction groupWaldhausen A-theory

MSC classification

Primary: 19B99: None of the above, but in this section
Secondary: 19G24: $L$-theory of group rings 20F36: Braid groups; Artin groups 57R67: Surgery obstructions, Wall groups 57N37: Isotopy and pseudo-isotopy
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 4 , August 2021 , pp. 1153 - 1170
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Copyright
© Canadian Mathematical Society 2020

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